If f '(x) = x4, what is f(x)? (Use C for the constant of integration.) f(x) =

Q: 3. y'-5y = x*e* - xe* – xe³x

A: 3. the given differential equation is y'-5y=x2ex-xe5x

Q: The number of internet users in a country increases at a rate that is jointly proportional to the…

A: Let number of people having personal computer be C(constant), number of people having internet be N.…

Q: To apply the integration factor method, does the differential equation have to be linear?

A:

Q: Find the differential equation of straight lines with slope and x –intercept equal.

A: Recall:  The equation of straight line is y=mx+b where, m=slope, b=y-intecept   Given, slope and x…

Q: What is a separable differential equation? How do yousolve it?

A: In a separable differential equation, we separate the variables and then take the integration of…

Q: y using an integrating factor, find the general solution of the differential equation dy/dx…

A: Given differential equation :                          dydx-ytanx=sinx

Q: Find the differential equation (Family of Curves): Lines with slope equal to the negative reciprocal…

A: Please check step 2 for solution.

Q: Use integration to find a general solution of the differential equation               dy / dx = 12x2

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Q: Solve for the differential of y when y= sinzx. x=-, and dx = - 3 2

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Q: Find the value of the arbitrary constant of the particular solution of the differential equation…

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Q: Find the general solution of the differential equation (4 + tan2 x)y′ = sec2 x

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Q: Use integration to find a general solution of the differential equation                      dy / dx…

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Q: Obtain the differential equation by eliminating all arbitrary constant.

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Q: From the differential equation by elimaniting arbitary constant y =ax'+ bx²

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Q: Find the differential equation of all straight lines at 2- unit distance from the origin.

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Q: Find the 3rd derivative of y = xlnx. (SOLVE BY USING DIFFERENTIAL EQUATIONS)

A: Given : f(x) =y= x lnx To find : Third derivative of given function

Q: Assume that a population P of wolves in a region is proportional to the area A of the region. Does…

A:

Q: a particular solution that satisfies the differential equation F'(x)=3x^2 +2x -1 and the inital

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Q: From the differential equation by elimaniting arbitary constant  y=ax3+bx2

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Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Solve the differential equation by variation of parameters. y" - y = cosh(x) y(x) =

A:

Q: Find the general solution to the differential equation y = x* tan(y) y = help (formulas) Use the…

A: Recall: ∫xn dx=xn+1n+1+C ∫cosxsinx dx= lnsin(x)+C ; Where C is integration constant. In this…

Q: Obtain the differential equation of the family of straight lines with slope and y-intercept equal.

A: Equation of straight line: y=mx+c Where, m = slope  c = y-intercept

Q: Use integration to find a general solution of the differential equation

A: Given: dydx = xex2  To find: General solution of the given differential equation.

Q: Solve the differential equation by variation of parameters. y" - y = cosh x y(x) II

A:

Q: al csc x y cotx

A: We have to find the intregating factor of given differential equation.

Q: Obtain the differential equation of the family of straight lines passing through (0,-1).

A: To Obtain the differential equation of the family of straight lines passing through (0,-1).

Q: Solve using the undermined coefficient of differential equation

A:

Q: 6. Why is it very easy to conclude that x2 dx diverges without making any integration calculations?

A: This question is taken from the calculus and sub-topic is improper integral in which we have to give…

Q: 6x2 dy dx'

A:

Q: What is the appropriate μ(x) integration factor of the equal linear differential equation?…

A:

Q: The integrating factor of non-exact differential equation (x°y³ – ®)dx – (y6 – x³y)dy = 0 - -

A:

Q: Find the differential equation having the solution as the equation representing all lines with slope…

A: Consider the family of straight lines with slope m and y-intercept c in slope-intercept form as,…

Q: Use separation of variables to find the general solution of the differential equation. (9 + x)y' =…

A: We have,

Q: A normal is drawn at a point P (x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A: We will show that the given differential equation describing such curve is correct and will find the…

Q: 3. What is a constant of integration? Why does an answer to an integration problem involve a…

A: Integration

Q: what is the differential coefficient of x.

A: To find differential coefficient of x we need to differentiate x with respect to x.

Q: Obtain the differential equation for the family of straight lines with x-intercept and y-intercept…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. The…

Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

A:

Q: Show that OW

A: x2+y2-xdx-ydy=0x2+y2-xdx+-ydy=0                 -Equation1Let M=x2+y2-x and N=-y∂M∂y=2y , ∂N∂x=0As…

Q: From the differential equation by elimanating arbitary constants  y=ax3+bx2

A:

Q: Describe the separation-of-variables technique for obtainingthe solution to a differential equation.

A: To describe the separation of variable technique.

Q: What is the differential equation of family of parabolas with vertex on the x – axis and axis…

A: General equation of parabola parallel to y-axis and having center (h, k) and having distance 'a'…

Q: Use integration to find a general solution of the differential equation       dy/dx = 2e3x

A: Consider the given differential equation as dydx=2e3x

Q: Calculate the truncation error to solve the differential equation: Yi+1¬Yi = Xị → (*) Ax dy Instead…

A: Follow the following solutions to get the complete correct answer.